PROBLEMS ORIGINATING FROM THE USE OF THE GORDON-SCHOWALTER DERIVATIVEIN THE JOHNSON-SEGALMAN AND RELATED MODELS IN VARIOUS SHEAR-FLOW SITUATIONS

The predictions of the Johnson-Segalman model have been compared to ex perimental results in some simple flows, namely steady state shearing flow and stress growth in shear, for various molten polyethylenes havi ng different molecular characteristics as far as their molecular weigh t level, polydispersity index and branching degree are concerned. Atte ntion has been focused on this particular model because it has been sh own to be an approximation of the Phan-Thien-Tanner equation in simple shear flows, the later model being frequently used in numerical calcu lations for complex flows. The Johnson-Segalman model is a codeformati onal rheological equation of state, which allows non-affine motion of the network junctions by introduction of a single parameter (a) named the slip factor. This assumption provides a great improvement in the p redictions of non-linear response to flows involving large deformation s, either in shear or in elongation. However, the determination of the slip parameter from the various experiments has shown that a single v alue of the slip factor can not be used to describe both tangential st resses (tau12) and normal stresses (tau11 - tau22) in polyethylene mel ts. This has been related to a discrepancy of the model concerning the violation of the Lodge-Meissner rule as a consequence of the use of t he Gordon-Schowalter derivative. Similar discrepancy can be expected i n the case of the Phan-Thien-Tanner equation. Nevertheless, the slip f actor, that can be determined either by fitting tangential stresses or normal stresses, is found to be nearly constant for a particular mate rial, whatever the flow regime is (transient or steady). Moreover, for the various linear polymers (high density or linear low density polye thylenes), these parameters appear to be nearly independent of the mol ecular weight distribution. In this case, the differences in the non-l inear behaviour in shear can only be attributed to differences in the linear relaxation modulus. On the other hand, a highly branched materi al (low density polyethylene) shows very different values of the slip parameters.